MinT - Best Known (53, 53+51, s)-Nets in Base 5

Best Known (53, 53+51, s)-Nets in Base 5

(53, 53+51, 82)-Net over F₅ — Constructive and digital

Digital (53, 104, 82)-net over F₅, using

t-expansion [i] based on digital (48, 104, 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]

(53, 53+51, 115)-Net over F₅ — Digital

Digital (53, 104, 115)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+51, 1910)-Net in Base 5 — Upper bound on s

There is no (53, 104, 1911)-net in base 5, because

1 times m-reduction [i] would yield (53, 103, 1911)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 989051 959220 019305 090021 343230 916454 566868 843664 834228 780386 899985 436029 > 5¹⁰³ [i]