MinT - Best Known (67, 143, s)-Nets in Base 5

Best Known (67, 143, s)-Nets in Base 5

(67, 143, 82)-Net over F₅ — Constructive and digital

Digital (67, 143, 82)-net over F₅, using

t-expansion [i] based on digital (48, 143, 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]

(67, 143, 132)-Net over F₅ — Digital

Digital (67, 143, 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]

(67, 143, 1575)-Net in Base 5 — Upper bound on s

There is no (67, 143, 1576)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9031 200095 285490 297718 931700 268745 584488 121102 600503 262608 256634 248938 056727 478673 652055 351200 631425 > 5¹⁴³ [i]