MinT - Best Known (132−36, 132, s)-Nets in Base 5

Best Known (132−36, 132, s)-Nets in Base 5

(132−36, 132, 408)-Net over F₅ — Constructive and digital

Digital (96, 132, 408)-net over F₅, using

trace code for nets [i] based on digital (30, 66, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(132−36, 132, 1522)-Net over F₅ — Digital

Digital (96, 132, 1522)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−36, 132, 252247)-Net in Base 5 — Upper bound on s

There is no (96, 132, 252248)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 671109 836836 252942 400413 973441 194811 012421 837214 354081 588398 356864 817068 008104 052417 554305 > 5¹³² [i]