MinT - Best Known (125−62, 125, s)-Nets in Base 5

Best Known (125−62, 125, s)-Nets in Base 5

(125−62, 125, 82)-Net over F₅ — Constructive and digital

Digital (63, 125, 82)-net over F₅, using

t-expansion [i] based on digital (48, 125, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(125−62, 125, 128)-Net over F₅ — Digital

Digital (63, 125, 128)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−62, 125, 2020)-Net in Base 5 — Upper bound on s

There is no (63, 125, 2021)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2352 365379 660543 758229 544104 427188 477423 548224 674347 795330 810049 756364 076217 144672 368925 > 5¹²⁵ [i]