MinT - Best Known (137−76, 137, s)-Nets in Base 5

Best Known (137−76, 137, s)-Nets in Base 5

(137−76, 137, 82)-Net over F₅ — Constructive and digital

Digital (61, 137, 82)-net over F₅, using

t-expansion [i] based on digital (48, 137, 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]

(137−76, 137, 120)-Net over F₅ — Digital

Digital (61, 137, 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]

(137−76, 137, 1215)-Net in Base 5 — Upper bound on s

There is no (61, 137, 1216)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 575416 230337 207459 675208 109234 210295 814644 233840 294849 742390 448400 768373 011372 250494 180166 155265 > 5¹³⁷ [i]