MinT - Best Known (63, 63+49, s)-Nets in Base 5

Best Known (63, 63+49, s)-Nets in Base 5

(63, 63+49, 132)-Net over F₅ — Constructive and digital

Digital (63, 112, 132)-net over F₅, using

6 times m-reduction [i] based on digital (63, 118, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 59, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(63, 63+49, 181)-Net over F₅ — Digital

Digital (63, 112, 181)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+49, 4170)-Net in Base 5 — Upper bound on s

There is no (63, 112, 4171)-net in base 5, because

1 times m-reduction [i] would yield (63, 111, 4171)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 385543 381578 273496 271287 971949 751673 633152 349689 134282 801813 934134 776643 749025 > 5¹¹¹ [i]