MinT - Best Known (150−71, 150, s)-Nets in Base 5

Best Known (150−71, 150, s)-Nets in Base 5

(150−71, 150, 132)-Net over F₅ — Constructive and digital

Digital (79, 150, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 75, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(150−71, 150, 176)-Net over F₅ — Digital

Digital (79, 150, 176)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−71, 150, 3261)-Net in Base 5 — Upper bound on s

There is no (79, 150, 3262)-net in base 5, because

1 times m-reduction [i] would yield (79, 149, 3262)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 926503 875652 541836 725681 683184 612438 715254 148727 063719 769208 720322 538000 042982 290431 384955 041325 643545 > 5¹⁴⁹ [i]