MinT - Best Known (70−53, 70, s)-Nets in Base 25

Best Known (70−53, 70, s)-Nets in Base 25

(70−53, 70, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 70, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 70, 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]

(70−53, 70, 150)-Net over F₂₅ — Digital

Digital (17, 70, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 70, 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]

(70−53, 70, 2240)-Net in Base 25 — Upper bound on s

There is no (17, 70, 2241)-net in base 25, because

1 times m-reduction [i] would yield (17, 69, 2241)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 880734 028374 841065 835226 398537 520591 530043 887627 298876 844531 125860 911325 615452 930746 482704 689585 > 25⁶⁹ [i]