MinT - Best Known (138−90, 138, s)-Nets in Base 5

Best Known (138−90, 138, s)-Nets in Base 5

(138−90, 138, 82)-Net over F₅ — Constructive and digital

Digital (48, 138, 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]

(138−90, 138, 92)-Net over F₅ — Digital

Digital (48, 138, 92)-net over F₅, using

t-expansion [i] based on digital (47, 138, 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]

(138−90, 138, 580)-Net in Base 5 — Upper bound on s

There is no (48, 138, 581)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 954823 149017 131453 943436 640348 147929 295728 509189 973416 095566 128449 193608 156870 301506 525580 347685 > 5¹³⁸ [i]