MinT - Best Known (107, 138, s)-Nets in Base 4

Best Known (107, 138, s)-Nets in Base 4

(107, 138, 1040)-Net over F₄ — Constructive and digital

Digital (107, 138, 1040)-net over F₄, using

4² times duplication [i] based on digital (105, 136, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 34, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(107, 138, 2376)-Net over F₄ — Digital

Digital (107, 138, 2376)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 138, 675230)-Net in Base 4 — Upper bound on s

There is no (107, 138, 675231)-net in base 4, because

1 times m-reduction [i] would yield (107, 137, 675231)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30354 324283 717443 879293 493791 014555 320944 477169 961700 337682 591386 028465 309817 542948 > 4¹³⁷ [i]