MinT - Best Known (63−35, 63, s)-Nets in Base 25

Best Known (63−35, 63, s)-Nets in Base 25

(63−35, 63, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 63, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 63, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(63−35, 63, 219)-Net over F₂₅ — Digital

Digital (28, 63, 219)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−35, 63, 37497)-Net in Base 25 — Upper bound on s

There is no (28, 63, 37498)-net in base 25, because

1 times m-reduction [i] would yield (28, 62, 37498)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 470 299666 753980 890210 583064 337863 013576 568951 535482 345323 929073 514427 638093 684320 657521 > 25⁶² [i]