MinT - Best Known (134−49, 134, s)-Nets in Base 5

Best Known (134−49, 134, s)-Nets in Base 5

(134−49, 134, 252)-Net over F₅ — Constructive and digital

Digital (85, 134, 252)-net over F₅, using

16 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 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]

(134−49, 134, 409)-Net over F₅ — Digital

Digital (85, 134, 409)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−49, 134, 18295)-Net in Base 5 — Upper bound on s

There is no (85, 134, 18296)-net in base 5, because

1 times m-reduction [i] would yield (85, 133, 18296)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 918 846922 806281 506070 206889 878060 492779 937613 683533 418812 851487 209259 144497 459634 117544 705025 > 5¹³³ [i]