MinT - Best Known (48, 48+82, s)-Nets in Base 5

Best Known (48, 48+82, s)-Nets in Base 5

(48, 48+82, 82)-Net over F₅ — Constructive and digital

Digital (48, 130, 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]

(48, 48+82, 92)-Net over F₅ — Digital

Digital (48, 130, 92)-net over F₅, using

t-expansion [i] based on digital (47, 130, 92)-net over F₅, using
- net from sequence [i] based on digital (47, 91)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(48, 48+82, 634)-Net in Base 5 — Upper bound on s

There is no (48, 130, 635)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 754624 245126 384376 763861 312234 446196 477357 719053 002555 276877 452260 702977 656294 858361 570125 > 5¹³⁰ [i]