MinT - Best Known (133−70, 133, s)-Nets in Base 5

Best Known (133−70, 133, s)-Nets in Base 5

(133−70, 133, 82)-Net over F₅ — Constructive and digital

Digital (63, 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]

(133−70, 133, 120)-Net over F₅ — Digital

Digital (63, 133, 120)-net over F₅, using

t-expansion [i] based on digital (61, 133, 120)-net over F₅, using
- net from sequence [i] based on digital (61, 119)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 61 and N(F) ≥ 120, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(133−70, 133, 1549)-Net in Base 5 — Upper bound on s

There is no (63, 133, 1550)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 930 002595 770887 533355 710190 700323 172839 660953 661763 882762 884325 342972 888653 803021 339198 295129 > 5¹³³ [i]