MinT - Best Known (70, 70+59, s)-Nets in Base 5

Best Known (70, 70+59, s)-Nets in Base 5

(70, 70+59, 132)-Net over F₅ — Constructive and digital

Digital (70, 129, 132)-net over F₅, using

3 times m-reduction [i] based on digital (70, 132, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 66, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(70, 70+59, 174)-Net over F₅ — Digital

Digital (70, 129, 174)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+59, 3528)-Net in Base 5 — Upper bound on s

There is no (70, 129, 3529)-net in base 5, because

1 times m-reduction [i] would yield (70, 128, 3529)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 295494 091534 621014 633284 468115 921793 390015 059169 601426 392408 498266 214643 457652 461906 179445 > 5¹²⁸ [i]