MinT - Best Known (138−32, 138, s)-Nets in Base 4

Best Known (138−32, 138, s)-Nets in Base 4

(138−32, 138, 1036)-Net over F₄ — Constructive and digital

Digital (106, 138, 1036)-net over F₄, using

4² 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]

(138−32, 138, 1997)-Net over F₄ — Digital

Digital (106, 138, 1997)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−32, 138, 353320)-Net in Base 4 — Upper bound on s

There is no (106, 138, 353321)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 121418 280997 354821 332035 439981 566558 959334 368149 940896 488710 321416 253344 144880 074194 > 4¹³⁸ [i]