MinT - Best Known (138−33, 138, s)-Nets in Base 4

Best Known (138−33, 138, s)-Nets in Base 4

(138−33, 138, 1032)-Net over F₄ — Constructive and digital

Digital (105, 138, 1032)-net over F₄, using

4² times duplication [i] based on digital (103, 136, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 34, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(138−33, 138, 1699)-Net over F₄ — Digital

Digital (105, 138, 1699)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−33, 138, 323995)-Net in Base 4 — Upper bound on s

There is no (105, 138, 323996)-net in base 4, because

1 times m-reduction [i] would yield (105, 137, 323996)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30354 989260 356125 451904 122461 739032 183878 681348 784009 480518 438347 473383 368191 749279 > 4¹³⁷ [i]