MinT - Best Known (23, 23+68, s)-Nets in Base 64

Best Known (23, 23+68, s)-Nets in Base 64

(23, 23+68, 177)-Net over F₆₄ — Constructive and digital

Digital (23, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 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]

(23, 23+68, 288)-Net in Base 64 — Constructive

(23, 91, 288)-net in base 64, using

t-expansion [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]

(23, 23+68, 342)-Net over F₆₄ — Digital

Digital (23, 91, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 91, 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]

(23, 23+68, 14649)-Net in Base 64 — Upper bound on s

There is no (23, 91, 14650)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 230 703419 368664 281209 089508 190624 459704 017854 532170 592697 731873 874729 669871 903564 909000 021964 223140 580735 083485 417190 714720 638894 345628 761405 025998 725347 446564 597444 > 64⁹¹ [i]