MinT - Best Known (147−84, 147, s)-Nets in Base 5

Best Known (147−84, 147, s)-Nets in Base 5

(147−84, 147, 82)-Net over F₅ — Constructive and digital

Digital (63, 147, 82)-net over F₅, using

t-expansion [i] based on digital (48, 147, 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]

(147−84, 147, 120)-Net over F₅ — Digital

Digital (63, 147, 120)-net over F₅, using

t-expansion [i] based on digital (61, 147, 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]

(147−84, 147, 1123)-Net in Base 5 — Upper bound on s

There is no (63, 147, 1124)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 789776 824636 366626 059532 231334 254199 092445 237997 278169 409455 905285 320638 339702 543481 145154 237948 436673 > 5¹⁴⁷ [i]