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

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

(73, 73+73, 93)-Net over F₅ — Constructive and digital

Digital (73, 146, 93)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (6, 42, 21)-net over F₅, using
  - net from sequence [i] based on digital (6, 20)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 6 and N(F) ≥ 21, 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]

(73, 73+73, 142)-Net over F₅ — Digital

Digital (73, 146, 142)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+73, 2306)-Net in Base 5 — Upper bound on s

There is no (73, 146, 2307)-net in base 5, because

1 times m-reduction [i] would yield (73, 145, 2307)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224486 044433 859415 342085 324177 571380 622774 620703 273377 673541 081340 426816 774419 602728 789937 241160 728305 > 5¹⁴⁵ [i]