MinT - Best Known (77−59, 77, s)-Nets in Base 128

Best Known (77−59, 77, s)-Nets in Base 128

(77−59, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (18, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 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]

(77−59, 77, 386)-Net over F₁₂₈ — Digital

Digital (18, 77, 386)-net over F₁₂₈, using

t-expansion [i] based on digital (15, 77, 386)-net over F₁₂₈, using
- net from sequence [i] based on digital (15, 385)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]

(77−59, 77, 30581)-Net in Base 128 — Upper bound on s

There is no (18, 77, 30582)-net in base 128, because

1 times m-reduction [i] would yield (18, 76, 30582)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14064 927075 527246 608581 113641 946675 889689 440911 849470 088070 449353 404675 704297 677777 876775 740392 541625 692582 279446 410387 113504 453411 408580 862727 328607 189613 521188 > 128⁷⁶ [i]