MinT - Best Known (72, 72+76, s)-Nets in Base 5

Best Known (72, 72+76, s)-Nets in Base 5

(72, 72+76, 88)-Net over F₅ — Constructive and digital

Digital (72, 148, 88)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (3, 41, 16)-net over F₅, using
  - net from sequence [i] based on digital (3, 15)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 3 and N(F) ≥ 16, using
      - an explicitly constructive algebraic function field [i]
2. digital (31, 107, 72)-net over F₅, using
  - net from sequence [i] based on digital (31, 71)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
      - an explicitly constructive algebraic function field [i]

(72, 72+76, 132)-Net over F₅ — Digital

Digital (72, 148, 132)-net over F₅, using

t-expansion [i] based on digital (67, 148, 132)-net over F₅, using
- net from sequence [i] based on digital (67, 131)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 67 and N(F) ≥ 132, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(72, 72+76, 1953)-Net in Base 5 — Upper bound on s

There is no (72, 148, 1954)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 28 088629 062395 947206 732246 439137 152193 204135 014108 141021 207883 585991 069684 508126 742837 145211 915800 553985 > 5¹⁴⁸ [i]