MinT - Best Known (84−63, 84, s)-Nets in Base 64

Best Known (84−63, 84, s)-Nets in Base 64

(84−63, 84, 177)-Net over F₆₄ — Constructive and digital

Digital (21, 84, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 84, 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]

(84−63, 84, 288)-Net in Base 64 — Constructive

(21, 84, 288)-net in base 64, using

base change [i] based on digital (9, 72, 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]

(84−63, 84, 342)-Net over F₆₄ — Digital

Digital (21, 84, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 84, 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]

(84−63, 84, 13492)-Net in Base 64 — Upper bound on s

There is no (21, 84, 13493)-net in base 64, because

1 times m-reduction [i] would yield (21, 83, 13493)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 819114 834457 537244 754457 368995 638957 987705 055968 452981 167330 192160 087458 350451 484519 911598 876363 148273 736522 247589 334772 562157 034957 491343 351225 225760 > 64⁸³ [i]