MinT - Best Known (7, 7+66, s)-Nets in Base 128

Best Known (7, 7+66, s)-Nets in Base 128

(7, 7+66, 216)-Net over F₁₂₈ — Constructive and digital

Digital (7, 73, 216)-net over F₁₂₈, using

t-expansion [i] based on digital (5, 73, 216)-net over F₁₂₈, using
- net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(7, 7+66, 262)-Net over F₁₂₈ — Digital

Digital (7, 73, 262)-net over F₁₂₈, using

net from sequence [i] based on digital (7, 261)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 7 and N(F) ≥ 262, using
  - a curve from the manYPoints database [i]

(7, 7+66, 4736)-Net in Base 128 — Upper bound on s

There is no (7, 73, 4737)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 6722 441774 880745 205877 665466 839023 896037 464032 910326 735193 715545 617707 216721 608015 115482 655125 355514 274927 155657 046966 422362 704079 500418 897321 333361 666432 > 128⁷³ [i]