MinT - Best Known (149−63, 149, s)-Nets in Base 5

Best Known (149−63, 149, s)-Nets in Base 5

(149−63, 149, 252)-Net over F₅ — Constructive and digital

Digital (86, 149, 252)-net over F₅, using

t-expansion [i] based on digital (85, 149, 252)-net over F₅, using
- 1 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]

(149−63, 149, 260)-Net over F₅ — Digital

Digital (86, 149, 260)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−63, 149, 6722)-Net in Base 5 — Upper bound on s

There is no (86, 149, 6723)-net in base 5, because

1 times m-reduction [i] would yield (86, 148, 6723)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 100932 443092 652174 222057 323152 950114 217133 309980 660464 484607 906428 380417 940746 952123 240863 639783 818581 > 5¹⁴⁸ [i]