MinT - Best Known (100, 100+45, s)-Nets in Base 4

Best Known (100, 100+45, s)-Nets in Base 4

(100, 100+45, 312)-Net over F₄ — Constructive and digital

Digital (100, 145, 312)-net over F₄, using

4¹ times duplication [i] based on digital (99, 144, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 48, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(100, 100+45, 554)-Net over F₄ — Digital

Digital (100, 145, 554)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+45, 26314)-Net in Base 4 — Upper bound on s

There is no (100, 145, 26315)-net in base 4, because

1 times m-reduction [i] would yield (100, 144, 26315)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 560973 374974 223758 985133 697878 672697 320078 707487 151668 689323 476587 077056 998657 375336 > 4¹⁴⁴ [i]