MinT - Best Known (126−49, 126, s)-Nets in Base 5

Best Known (126−49, 126, s)-Nets in Base 5

(126−49, 126, 252)-Net over F₅ — Constructive and digital

Digital (77, 126, 252)-net over F₅, using

8 times m-reduction [i] based on digital (77, 134, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 67, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(126−49, 126, 306)-Net over F₅ — Digital

Digital (77, 126, 306)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(126−49, 126, 10692)-Net in Base 5 — Upper bound on s

There is no (77, 126, 10693)-net in base 5, because

1 times m-reduction [i] would yield (77, 125, 10693)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2355 906276 449790 795369 871357 172043 253416 975654 031449 764762 507869 257823 418113 933147 672225 > 5¹²⁵ [i]