MinT - Best Known (85−69, 85, s)-Nets in Base 25

Best Known (85−69, 85, s)-Nets in Base 25

(85−69, 85, 126)-Net over F₂₅ — Constructive and digital

Digital (16, 85, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 85, 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]

(85−69, 85, 150)-Net over F₂₅ — Digital

Digital (16, 85, 150)-net over F₂₅, using

net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
  - an algebraic function field by Teo [i]

(85−69, 85, 1585)-Net in Base 25 — Upper bound on s

There is no (16, 85, 1586)-net in base 25, because

1 times m-reduction [i] would yield (16, 84, 1586)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2708 842868 422192 859962 668951 257710 528840 242803 601361 293358 289336 512624 059824 773400 338214 455765 408451 751359 314213 967905 > 25⁸⁴ [i]