MinT - Best Known (116−57, 116, s)-Nets in Base 5

Best Known (116−57, 116, s)-Nets in Base 5

(116−57, 116, 82)-Net over F₅ — Constructive and digital

Digital (59, 116, 82)-net over F₅, using

t-expansion [i] based on digital (48, 116, 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]

(116−57, 116, 125)-Net over F₅ — Digital

Digital (59, 116, 125)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−57, 116, 2077)-Net in Base 5 — Upper bound on s

There is no (59, 116, 2078)-net in base 5, because

1 times m-reduction [i] would yield (59, 115, 2078)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 243 543139 180566 664298 746457 055998 654726 931908 686574 538821 267510 475589 017895 296705 > 5¹¹⁵ [i]