MinT - Best Known (54, 54+66, s)-Nets in Base 5

Best Known (54, 54+66, s)-Nets in Base 5

(54, 54+66, 82)-Net over F₅ — Constructive and digital

Digital (54, 120, 82)-net over F₅, using

t-expansion [i] based on digital (48, 120, 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]

(54, 54+66, 104)-Net over F₅ — Digital

Digital (54, 120, 104)-net over F₅, using

t-expansion [i] based on digital (51, 120, 104)-net over F₅, using
- net from sequence [i] based on digital (51, 103)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 51 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(54, 54+66, 1121)-Net in Base 5 — Upper bound on s

There is no (54, 120, 1122)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 764260 799577 341186 591595 054654 350710 371086 611192 719114 366733 444272 231583 790389 763465 > 5¹²⁰ [i]