MinT - Best Known (133−80, 133, s)-Nets in Base 5

Best Known (133−80, 133, s)-Nets in Base 5

(133−80, 133, 82)-Net over F₅ — Constructive and digital

Digital (53, 133, 82)-net over F₅, using

t-expansion [i] based on digital (48, 133, 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]

(133−80, 133, 104)-Net over F₅ — Digital

Digital (53, 133, 104)-net over F₅, using

t-expansion [i] based on digital (51, 133, 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]

(133−80, 133, 802)-Net in Base 5 — Upper bound on s

There is no (53, 133, 803)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 951 644193 327943 882415 467778 453393 166127 337276 989054 608362 501695 745023 213298 640702 345505 922145 > 5¹³³ [i]