MinT - Best Known (55, 55+50, s)-Nets in Base 5

Best Known (55, 55+50, s)-Nets in Base 5

(55, 55+50, 82)-Net over F₅ — Constructive and digital

Digital (55, 105, 82)-net over F₅, using

t-expansion [i] based on digital (48, 105, 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]

(55, 55+50, 128)-Net over F₅ — Digital

Digital (55, 105, 128)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(55, 55+50, 2175)-Net in Base 5 — Upper bound on s

There is no (55, 105, 2176)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 24 702324 933770 616868 910368 135574 658276 563338 112977 187325 065614 970691 174913 > 5¹⁰⁵ [i]