MinT - Best Known (92, 92+51, s)-Nets in Base 5

Best Known (92, 92+51, s)-Nets in Base 5

(92, 92+51, 296)-Net over F₅ — Constructive and digital

Digital (92, 143, 296)-net over F₅, using

3 times m-reduction [i] based on digital (92, 146, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 73, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(92, 92+51, 478)-Net over F₅ — Digital

Digital (92, 143, 478)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 92+51, 23734)-Net in Base 5 — Upper bound on s

There is no (92, 143, 23735)-net in base 5, because

1 times m-reduction [i] would yield (92, 142, 23735)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1794 435252 256675 921461 888269 793701 345769 405000 403290 009950 790250 254645 080610 645270 516284 494755 897981 > 5¹⁴² [i]