MinT - Best Known (150−85, 150, s)-Nets in Base 5

Best Known (150−85, 150, s)-Nets in Base 5

(150−85, 150, 82)-Net over F₅ — Constructive and digital

Digital (65, 150, 82)-net over F₅, using

t-expansion [i] based on digital (48, 150, 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]

(150−85, 150, 120)-Net over F₅ — Digital

Digital (65, 150, 120)-net over F₅, using

t-expansion [i] based on digital (61, 150, 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]

(150−85, 150, 1214)-Net in Base 5 — Upper bound on s

There is no (65, 150, 1215)-net in base 5, because

1 times m-reduction [i] would yield (65, 149, 1215)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 159732 392452 219419 188331 483511 962010 585914 117162 361972 915156 002196 497024 386514 119154 539842 728347 594585 > 5¹⁴⁹ [i]