MinT - Best Known (113−50, 113, s)-Nets in Base 4

Best Known (113−50, 113, s)-Nets in Base 4

(113−50, 113, 130)-Net over F₄ — Constructive and digital

Digital (63, 113, 130)-net over F₄, using

1 times m-reduction [i] based on digital (63, 114, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 57, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(113−50, 113, 1765)-Net in Base 4 — Upper bound on s

There is no (63, 113, 1766)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 108 619871 685488 493603 792648 906808 648140 424330 360556 671414 107984 004804 > 4¹¹³ [i]