MinT - Best Known (63, 63+74, s)-Nets in Base 5

Best Known (63, 63+74, s)-Nets in Base 5

(63, 63+74, 82)-Net over F₅ — Constructive and digital

Digital (63, 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]

(63, 63+74, 120)-Net over F₅ — Digital

Digital (63, 137, 120)-net over F₅, using

t-expansion [i] based on 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]

(63, 63+74, 1391)-Net in Base 5 — Upper bound on s

There is no (63, 137, 1392)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 577519 802287 537737 164807 028866 584130 096617 278274 468610 874414 439550 994426 877293 783785 033565 631425 > 5¹³⁷ [i]