MinT - Best Known (146−50, 146, s)-Nets in Base 5

Best Known (146−50, 146, s)-Nets in Base 5

(146−50, 146, 296)-Net over F₅ — Constructive and digital

Digital (96, 146, 296)-net over F₅, using

t-expansion [i] based on digital (94, 146, 296)-net over F₅, using
- 4 times m-reduction [i] based on digital (94, 150, 296)-net over F₅, using
  - trace code for nets [i] based on digital (19, 75, 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]

(146−50, 146, 576)-Net over F₅ — Digital

Digital (96, 146, 576)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−50, 146, 30710)-Net in Base 5 — Upper bound on s

There is no (96, 146, 30711)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121119 083206 791112 557142 158637 295615 820829 615290 524560 901568 983523 359737 505340 586706 792898 246489 427837 > 5¹⁴⁶ [i]