MinT - Best Known (150−68, 150, s)-Nets in Base 5

Best Known (150−68, 150, s)-Nets in Base 5

(150−68, 150, 132)-Net over F₅ — Constructive and digital

Digital (82, 150, 132)-net over F₅, using

t-expansion [i] based on 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]

(150−68, 150, 204)-Net over F₅ — Digital

Digital (82, 150, 204)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−68, 150, 4078)-Net in Base 5 — Upper bound on s

There is no (82, 150, 4079)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 705 878213 928135 356242 538885 722239 328319 934586 851663 405180 257831 069110 306086 623380 869111 089705 765894 338425 > 5¹⁵⁰ [i]