MinT - Best Known (105, 137, s)-Nets in Base 4

Best Known (105, 137, s)-Nets in Base 4

(105, 137, 1036)-Net over F₄ — Constructive and digital

Digital (105, 137, 1036)-net over F₄, using

4¹ times duplication [i] based on digital (104, 136, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 34, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(105, 137, 1910)-Net over F₄ — Digital

Digital (105, 137, 1910)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 137, 323995)-Net in Base 4 — Upper bound on s

There is no (105, 137, 323996)-net in base 4, because

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]