MinT - Best Known (59, 59+55, s)-Nets in Base 5

Best Known (59, 59+55, s)-Nets in Base 5

(59, 59+55, 82)-Net over F₅ — Constructive and digital

Digital (59, 114, 82)-net over F₅, using

t-expansion [i] based on digital (48, 114, 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]

(59, 59+55, 131)-Net over F₅ — Digital

Digital (59, 114, 131)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+55, 2279)-Net in Base 5 — Upper bound on s

There is no (59, 114, 2280)-net in base 5, because

1 times m-reduction [i] would yield (59, 113, 2280)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 631740 567866 020191 530251 426039 949863 060787 802119 754347 186974 926799 044226 042529 > 5¹¹³ [i]