MinT - Best Known (150−55, 150, s)-Nets in Base 5

Best Known (150−55, 150, s)-Nets in Base 5

(150−55, 150, 296)-Net over F₅ — Constructive and digital

Digital (95, 150, 296)-net over F₅, using

t-expansion [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]

(150−55, 150, 444)-Net over F₅ — Digital

Digital (95, 150, 444)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−55, 150, 19642)-Net in Base 5 — Upper bound on s

There is no (95, 150, 19643)-net in base 5, because

1 times m-reduction [i] would yield (95, 149, 19643)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 290312 194615 152603 771827 734403 952301 518246 696323 200965 268852 316756 328094 418247 280309 022640 906515 879365 > 5¹⁴⁹ [i]