MinT - Best Known (94, 94+35, s)-Nets in Base 5

Best Known (94, 94+35, s)-Nets in Base 5

(94, 94+35, 400)-Net over F₅ — Constructive and digital

Digital (94, 129, 400)-net over F₅, using

9 times m-reduction [i] based on digital (94, 138, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 69, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(94, 94+35, 1535)-Net over F₅ — Digital

Digital (94, 129, 1535)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+35, 328626)-Net in Base 5 — Upper bound on s

There is no (94, 129, 328627)-net in base 5, because

1 times m-reduction [i] would yield (94, 128, 328627)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 293887 867294 380106 388371 586717 063736 251301 321761 913208 300950 551752 966510 598723 393355 754125 > 5¹²⁸ [i]