MinT - Best Known (73, 73+71, s)-Nets in Base 5

Best Known (73, 73+71, s)-Nets in Base 5

(73, 73+71, 94)-Net over F₅ — Constructive and digital

Digital (73, 144, 94)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (7, 42, 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, 102, 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+71, 147)-Net over F₅ — Digital

Digital (73, 144, 147)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+71, 2468)-Net in Base 5 — Upper bound on s

There is no (73, 144, 2469)-net in base 5, because

1 times m-reduction [i] would yield (73, 143, 2469)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8979 195235 866501 234614 012247 501633 609566 598826 140278 048159 161768 700527 522453 475228 517635 824110 807501 > 5¹⁴³ [i]