MinT - Best Known (74, 74+73, s)-Nets in Base 5

Best Known (74, 74+73, s)-Nets in Base 5

(74, 74+73, 94)-Net over F₅ — Constructive and digital

Digital (74, 147, 94)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (7, 43, 22)-net over F₅, using
  - net from sequence [i] based on digital (7, 21)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 104, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(74, 74+73, 146)-Net over F₅ — Digital

Digital (74, 147, 146)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+73, 2413)-Net in Base 5 — Upper bound on s

There is no (74, 147, 2414)-net in base 5, because

1 times m-reduction [i] would yield (74, 146, 2414)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 127734 472832 413319 777266 565223 853817 991858 137945 465686 100769 336762 948207 980192 604211 338121 911503 651393 > 5¹⁴⁶ [i]