MinT - Best Known (100−54, 100, s)-Nets in Base 5

Best Known (100−54, 100, s)-Nets in Base 5

(100−54, 100, 78)-Net over F₅ — Constructive and digital

Digital (46, 100, 78)-net over F₅, using

t-expansion [i] based on digital (38, 100, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(100−54, 100, 88)-Net over F₅ — Digital

Digital (46, 100, 88)-net over F₅, using

t-expansion [i] based on digital (45, 100, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(100−54, 100, 1039)-Net in Base 5 — Upper bound on s

There is no (46, 100, 1040)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7900 971922 379956 212811 899153 004390 055215 993757 605092 684826 005528 810049 > 5¹⁰⁰ [i]