MinT - Best Known (138−49, 138, s)-Nets in Base 5

Best Known (138−49, 138, s)-Nets in Base 5

(138−49, 138, 296)-Net over F₅ — Constructive and digital

Digital (89, 138, 296)-net over F₅, using

2 times m-reduction [i] based on digital (89, 140, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 70, 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]

(138−49, 138, 472)-Net over F₅ — Digital

Digital (89, 138, 472)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−49, 138, 23929)-Net in Base 5 — Upper bound on s

There is no (89, 138, 23930)-net in base 5, because

1 times m-reduction [i] would yield (89, 137, 23930)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 574085 378318 393510 498894 987611 389157 792100 826827 098430 378573 047868 221156 374858 619438 363297 977985 > 5¹³⁷ [i]