MinT - Best Known (113−54, 113, s)-Nets in Base 5

Best Known (113−54, 113, s)-Nets in Base 5

(113−54, 113, 82)-Net over F₅ — Constructive and digital

Digital (59, 113, 82)-net over F₅, using

t-expansion [i] based on digital (48, 113, 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]

(113−54, 113, 134)-Net over F₅ — Digital

Digital (59, 113, 134)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−54, 113, 2279)-Net in Base 5 — Upper bound on s

There is no (59, 113, 2280)-net in base 5, because

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]