MinT - Best Known (149−75, 149, s)-Nets in Base 5

Best Known (149−75, 149, s)-Nets in Base 5

(149−75, 149, 93)-Net over F₅ — Constructive and digital

Digital (74, 149, 93)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (6, 43, 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, 106, 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]

(149−75, 149, 141)-Net over F₅ — Digital

Digital (74, 149, 141)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−75, 149, 2262)-Net in Base 5 — Upper bound on s

There is no (74, 149, 2263)-net in base 5, because

1 times m-reduction [i] would yield (74, 148, 2263)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 336248 106177 145819 007816 196906 160017 330330 313228 450831 464467 251722 508643 172300 593411 894082 115205 422285 > 5¹⁴⁸ [i]