MinT - Best Known (113−55, 113, s)-Nets in Base 5

Best Known (113−55, 113, s)-Nets in Base 5

(113−55, 113, 82)-Net over F₅ — Constructive and digital

Digital (58, 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]

(113−55, 113, 126)-Net over F₅ — Digital

Digital (58, 113, 126)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−55, 113, 2146)-Net in Base 5 — Upper bound on s

There is no (58, 113, 2147)-net in base 5, because

1 times m-reduction [i] would yield (58, 112, 2147)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 928086 643537 476068 849189 332258 576486 785517 056377 767033 578008 489844 824501 649125 > 5¹¹² [i]