MinT - Best Known (53, 53+84, s)-Nets in Base 5

Best Known (53, 53+84, s)-Nets in Base 5

(53, 53+84, 82)-Net over F₅ — Constructive and digital

Digital (53, 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]

(53, 53+84, 104)-Net over F₅ — Digital

Digital (53, 137, 104)-net over F₅, using

t-expansion [i] based on digital (51, 137, 104)-net over F₅, using
- net from sequence [i] based on digital (51, 103)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 51 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(53, 53+84, 755)-Net in Base 5 — Upper bound on s

There is no (53, 137, 756)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 575280 028439 369985 012688 714956 603308 203925 468565 005344 701455 617032 281975 410320 435739 095283 762625 > 5¹³⁷ [i]