MinT - Best Known (14, 77, s)-Nets in Base 128

Best Known (14, 77, s)-Nets in Base 128

(14, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (14, 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]

(14, 77, 353)-Net over F₁₂₈ — Digital

Digital (14, 77, 353)-net over F₁₂₈, using

net from sequence [i] based on digital (14, 352)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 14 and N(F) ≥ 353, using
  - a curve from the manYPoints database [i]

(14, 77, 14316)-Net in Base 128 — Upper bound on s

There is no (14, 77, 14317)-net in base 128, because

1 times m-reduction [i] would yield (14, 76, 14317)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14080 912386 045666 307531 145608 906749 066587 049313 757123 151254 442744 483654 908919 280572 942331 347300 444573 668634 875590 758747 553998 838658 732083 761689 718610 101436 933280 > 128⁷⁶ [i]