MinT - Best Known (133−39, 133, s)-Nets in Base 4

Best Known (133−39, 133, s)-Nets in Base 4

(133−39, 133, 384)-Net over F₄ — Constructive and digital

Digital (94, 133, 384)-net over F₄, using

4¹ times duplication [i] based on digital (93, 132, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 44, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(133−39, 133, 660)-Net over F₄ — Digital

Digital (94, 133, 660)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−39, 133, 40240)-Net in Base 4 — Upper bound on s

There is no (94, 133, 40241)-net in base 4, because

1 times m-reduction [i] would yield (94, 132, 40241)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 29 652331 730679 380478 650372 488972 507998 513229 201437 000160 875009 818218 008953 556832 > 4¹³² [i]