MinT - Best Known (157−49, 157, s)-Nets in Base 4

Best Known (157−49, 157, s)-Nets in Base 4

(157−49, 157, 312)-Net over F₄ — Constructive and digital

Digital (108, 157, 312)-net over F₄, using

4¹ times duplication [i] based on digital (107, 156, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 52, 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]

(157−49, 157, 578)-Net over F₄ — Digital

Digital (108, 157, 578)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−49, 157, 26749)-Net in Base 4 — Upper bound on s

There is no (108, 157, 26750)-net in base 4, because

1 times m-reduction [i] would yield (108, 156, 26750)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8347 732807 043618 074988 273883 677499 629346 617794 407498 170868 716132 233838 877404 061344 319659 151901 > 4¹⁵⁶ [i]