MinT - Best Known (63, 63+41, s)-Nets in Base 25

Best Known (63, 63+41, s)-Nets in Base 25

(63, 63+41, 378)-Net over F₂₅ — Constructive and digital

Digital (63, 104, 378)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (10, 23, 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]
2. digital (10, 30, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
3. digital (10, 51, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(63, 63+41, 2853)-Net over F₂₅ — Digital

Digital (63, 104, 2853)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+41, 5476274)-Net in Base 25 — Upper bound on s

There is no (63, 104, 5476275)-net in base 25, because

1 times m-reduction [i] would yield (63, 103, 5476275)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 972347 681863 722221 152711 745282 827471 639260 072482 214254 904351 677100 603235 994030 228398 016924 595872 195129 794663 875719 169759 118884 421264 506658 980001 > 25¹⁰³ [i]