MinT - Best Known (80−63, 80, s)-Nets in Base 25

Best Known (80−63, 80, s)-Nets in Base 25

(80−63, 80, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 80, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 80, 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]

(80−63, 80, 150)-Net over F₂₅ — Digital

Digital (17, 80, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 80, 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]

(80−63, 80, 1873)-Net in Base 25 — Upper bound on s

There is no (17, 80, 1874)-net in base 25, because

1 times m-reduction [i] would yield (17, 79, 1874)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 277 775407 832712 548879 319121 757369 406389 034389 812884 442640 416536 269975 454508 504542 836794 424183 515192 809689 219857 > 25⁷⁹ [i]