MinT - Best Known (89−66, 89, s)-Nets in Base 64

Best Known (89−66, 89, s)-Nets in Base 64

(89−66, 89, 177)-Net over F₆₄ — Constructive and digital

Digital (23, 89, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 89, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(89−66, 89, 288)-Net in Base 64 — Constructive

(23, 89, 288)-net in base 64, using

t-expansion [i] based on (22, 89, 288)-net in base 64, using
- 2 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
  - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(89−66, 89, 342)-Net over F₆₄ — Digital

Digital (23, 89, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 89, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(89−66, 89, 15515)-Net in Base 64 — Upper bound on s

There is no (23, 89, 15516)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56303 600875 406252 460668 722820 942620 268774 748149 847099 668112 261839 687568 369650 505534 643816 832716 594451 745228 927727 016091 134240 477659 576351 354076 106495 514495 753588 > 64⁸⁹ [i]